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10 minutes reading time (1938 words)

Teaching two-octave scales

I'm coming up on my fiftieth anniversary of teaching, and I've learned some painful lessons. Here's one: playing two-octave scales isn't twice as hard as playing scales in one octave; it's ten times more difficult. Here's another: you can never assume students grasp a concept, no matter how well they can demonstrate it in practice—and how many times you clarify. No, repeated explanations and "trying" won't do it all by themselves. You have to stress the basics.

I am a fanatic about fingering. In my opinion, bad or inconsistent fingering is the cause of lots of performance problems that we sometimes call by other names, such as rushing, memory slips, and persistent inaccuracy. I teach my students to be super-careful about their fingering, first, by being extremely finicky, and then by explaining key concepts as I go. The first concept relating to scale-playing is "scale degrees." A scale degree is the position of a note within a scale, counting from the bottom. Thus the note "C" is the first scale degree of C major, but the fourth scale degree of G major, and the fifth of F major.

How does this relate to scale playing? A basic principle of good fingering is to use the same fingers on patterns with the same musical content, whenever possible. Thus, if your right hand thumb plays the fourth scale degree on the first statement of a pattern, it should do the same every time that pattern recurs (if possible), no matter what key it is in.

A good example of this is what I call Group I major scales, which are C, G, D, A, and E. They follow this fingering pattern:

RH 

  • Thumb on the first & fourth scale degrees 
  • 4th finger on seventh scale degree

LH 

  • Thumb on the fifth & first scale degrees 
  • 4th finger on the second scale degree

Although teaching fingering using this system may seem cumbersome at first, it yields many benefits. First, the student has to think before she starts. Instead of just charging into the scale with a happy smile on her face (or not…), hoping for the best, she has to stop and think, "what is the fourth scale degree in this key, and what finger plays it?" Focusing on the thumb as part of this process is essential; many fingering problems, in technic as well as repertoire, are solved if the student knows what notes her thumb plays. Thinking in scale degrees will pay off in planning an interpretation, too, since emphasis (or lack of) on a particular scale degree is an important part of melodic shape and color.

Group II major scales are the enharmonic scales, B/C-flat, F-sharp/G-flat, and C-sharp/ D-flat. Yes, I do require students to spell them both ways. The fingering for this group reveals another important principle of fingering, what I call "C.P.E. Bach's Rule." In his book, Essay on the True Art of Playing Keyboard Instruments, Bach tells us (I'm paraphrasing) that the most comfortable fingering can always be found when you put long fingers (2,3,4) on short (black) notes, and short fingers (1,5) on long (white) notes.1 In the Group II scales, the fifth finger isn't used, so it's easy for the student to remember: thumbs play white keys. Interestingly, Chopin used the same principle in teaching his students, saying that they should start on what I call Group II scales since those scales more closely follow the natural hand position.

Group III scales are F, B-flat, E-flat, and A-flat. These scales also have their unifying characteristics.

RH

  • Thumb on the notes F & C; 4th finger always goes on B-flat. 

LH 

  • Thumb on scale degrees 3 & 7 
  • Fourth finger on scale degree 4

Note that this gives you an unconventional fingering in the LH for F major, starting on finger 3 instead of 5. I think this is much easier to play than the standard fingering, which starts on finger 5. Try it and see if you think I am right.

Getting back to painful teaching memories…yes, repeated explanations don't usually work. Getting the student to explain it to you himself does.

First, my student tells me the name of the scale (duh…but I've learned not to skip this step; see "painful lessons" above).

Next, he spells the scale from bottom-top, and top-bottom, following the pattern W-W-H-W-W-W-H.

Then, he tells me the key signature, listing the sharps or flats in order.

Many teachers use mnemonic devices, such as "Father Charles Goes Down And Eats Bread" for the sharps, and "BEAD Gum Candy Fruit" for flats, for instance.

I have a different plan. I teach sharps by starting on the note F and counting up by fifths; flats by starting on the note B and counting down by fifths. Why? It helps them develop facility in thinking in fifths, perhaps the most important interval in classical music. For the Group II scales (B/C-flat, F-sharp/G-flat, and C-sharp/D-flat), there is an interim step. I ask him to tell me the names of the white keys—remember, these are played by the thumb.

Finally, the student tells me the names of the notes he will play with his thumb and his fourth finger, in each hand.

Too much thinking and talking, and not enough playing? Not in my opinion. Remember Leschetizky's advice to his students: "Think ten times, then play once."

An important step to playing two-octave scales well is getting really good at playing one octave scales. I take my students through several steps.

Cross-hand scales  

  • Setup your right hand in pentascale position. 
  • Play the sixth scale degree on top, and the seventh scale degree on the bottom by crossing over with the LH
  • Reverse hands (see Excerpts 1 and 2).
I prefer this configuration to what some methods call "tetrachord scales." Musically, cross-hand scales prepare students for the way composers actually write scales in pieces: not in pure form. This particular way of writing (ascending scale, with the seventh scale degree dropping down an octave) was particularly favored by J.S. Bach when he wrote harmonic minor scales. Apparently, he did not care for the sound of the interval of the augmented second. Cross-hand scales are a good way to start teaching circular rotation, too.
Excerpt 1: “Cross-Hand Scales, Right Hand” by Scott McBride Smith.
Excerpt 2: “Cross-Hand Scales, Left Hand” by Scott McBride Smith.
Excerpt 3: “Complementary Patterns” by Scott McBride Smith, from American Popular Piano, Technic, Book 3.

One-octave scales 

  • In parallel and contrary motion 
  • Starting at the top as well as at the bottom 

One-octave scales in complementary patterns 

  • In parallel and contrary motion, but with different rhythmic values in each hand (see Excerpt 3)
I follow the same philosophy and procedures in teaching two-octave scales: parallel and contrary motion, starting at the top and at the bottom, and complementary rhythmic patterns. Once you understand the basic concept, there is no limit to what your own creativity—and the problems found in the pieces your students are preparing—can devise. You could have your students play staccato in the right hand, for example, and legato in the left. This is a great preparation for Bach's Invention in F Major, which is often performed with detached eighth-notes and legato sixteenths, occurring simultaneously.

I have an interim teaching— well, practice—approach that works well in the transition from one-octave to two-octave scales. I call this "Stop-and-Go Scales." Some of us of a certain age remember a game we enjoyed on the playground called, you guessed it, "Stop and Go," or sometimes "Red Light, Green Light." When the child who is chosen "it" says stop, all the other children must freeze; when "it" says go, they can move (there's more to it than this, but you don't need to know in order to utilize this practice device). Here's how I apply it to two-octave scales:

1) Ask the student to tell you, or write down, what notes the thumb plays, and what note the fourth finger plays in the chosen scale. The fourth finger is important in this context because, in most major scales, the fourth finger will only be used once, since a major scale consists of seven notes—a three-finger grouping and a four-finger grouping. In the exercise shown in Excerpt 4, they can fill in the blanks.

2) Insert a fermata, real or imaginary, on the note before the cross-over or cross-under. 

3) Play the scale, first hands alone and then together, and stop at each fermata. While holding the appropriate note down, say the name and finger number of the next note, which will be the final crossing note, "4 on B-fl at," for instance, or "1 on C." If your student knows the cross-overs and unders, there will be very few fingering mistakes—the other fingers simply follow in succession. This practice technic again reinforces Leschetizky's pithy saying, which I paraphrase as "listen—think—play."
Excerpt 4: “Stop and Go Scales” by Scott McBride Smith, from American Popular Piano, Technic, Book 3.


I will conclude by repeating what I stated at the end of Part I (see Sep/ Oct 2013): the single most important skill to playing scales is rotation. Remember we most often use single rotation in playing notes moving in the opposite direction (prepare laterally, play medially; play laterally; play medially…), with one rotational movement preparing for the next note. We also use single rotation when we are crossing. Students sometimes have difficulty grasping this, so I make up exercises that isolate the cross. See Excerpt 5 for an example.

Excerpt 5: Crossing example by Scott McBride Smith.

To play: 

  • Rotate medially, to prepare 
  • Play the note "E" with a lateral rotation 
  • Continue the rotation after striking "E," while holding "E" down lightly 
  • Your thumbnail should almost be pointing up 
  • This continuing motion serves as a lateral preparation to 
  • Play the note "F" medially.
Depending upon your student's size and finger length, he or she may, or may not, be able to play E–F legato. Don't worry about it— it's not crucial at this stage. 
  • Double rotation is necessary when notes move in the same direction, all up or all down.
If we play all the notes of a C major scale, we see the following rotation:

Ascending (RH) 
  • Prepare laterally
  • Play C with a single medial rotation
  • D with a double rotation
  • E with a double rotation
  • F with a single rotation
  • G with a double rotation
  • A with a double rotation
  • B with a double rotation
  • C with a double rotation (if it is the top note; a single rotation if you are continuing up another octave)
Descending (RH)
  • B with a single rotation, since you are changing direction
  • A with a double rotation
  • G with a double rotation
  • F with a double rotation
  • E with a single rotation
  • D with a double rotation
  • C with a double rotation
I said it before, and I'll say it again: as the student successively becomes more adept, the motions get faster, at faster speeds becoming almost invisible. But no matter what speed, rotation is a component of good passagework playing.

Confusing? Not so much, once you understand the principles. Remember, we're stressing the basics. Reading about technic is hard, writing about it even worse. I invite you to watch the video demonstration on this page. I promise, you'll understand everything!

1​ Bach, C.P.E. (1753). Essay on the True Art of Playing Keyboard Instruments (William Mitchell, Trans., 1948). New York: W.W. Norton.

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